3,128 Results Found

The existence of at least three bounded weak solutions is established for a nonlinear elliptic equation with unbounded coefficients. The approach is based on variational methods and critical point theorems.

By using some solvability methods and the contraction mapping principle are investigated bounded, as well as periodic solutions to some classes of nonhomogeneous linear second-order difference equations on domains ${\mathbb{N}}_0$ , $\mathbb{Z}\setminus {\mathbb{N}}_2$ and ...

This manuscript reanalyses the Bagley–Torvik equation (BTE). The Riemann–Liouville fractional differential equation (FDE), formulated by R. L. Bagley and P. J. Torvik in 1984, models the vertical motion of a thin plate immersed in a Newto...

In the present work, an initial boundary value problem (IBVP) for the semi-linear delay differential equation in a Banach space with unbounded positive operators is studied. The main theorem on the uniqueness and existence of a bounded solution (BS)...

Diophantine equations ${\displaystyle \prod }_{i=1}^n{x}_i=F{\displaystyle \sum }_{i=1}^n{x}_i$ with $x_i,F\in {\mathbb{Z}}^{+}$ associate the products and sums of n natural numbers. Only special cases have been studied so far. Here, we provide new parametric solutions depending on F and the divisors of F or F². One of these...

In this paper, applying some properties of matrix inequality and Schur complement, we give new upper and lower bounds of the solution for the unified algebraic Lyapunov equation that generalize the forms of discrete and continuous Lyapunov matrix equ...

Boundedness is an essential feature of the solutions for various mathematical and numerical models in the natural sciences, especially those systems in which linear or nonlinear preservation or stability features are fundamental. In those cases, the...

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons is modeled by a Riemann–Liouville fractional derivative with respect to another function and an appropriate initial condition is set up. Some inequ...

This study proposes a three-dimensional upper bound solution for estimating the soil thrust of tracked vehicles on saturated clay slopes. The present study considered block, triangular wedge, and trapezoidal wedge failure modes to formulate an upper...

We study a class of conformable time-fractional stochastic equation $T_{\alpha ,t}^{a}u(x,t)=\sigma \left(u(x,t)\right){\dot{W}}_t,x\in \mathbb{R},t\in [a,T],T<\infty ,0<\alpha <1.$ The initial con...

The purpose of this paper is to give new oscillation criteria for second-order delay differential equations $y^{″}\left(t\right)=p\left(t\right)y\left(\tau \left(t\right)\right).$ We introduce a new technique for the elimination of bounded nonoscillatory solutions.

Based on the eigenvalue idea and the time-varying weighted vector norm in the state space ${\mathbb{R}}^n$ we construct here the lower and upper bounds of the solutions of uniformly asymptotically stable linear systems. We generalize the known results for...

In this paper, we study the initial value problem for a semilinear delay hyperbolic equation in Hilbert spaces with a self-adjoint positive definite operator. The mean theorem on the existence and uniqueness of a bounded solution of this differential...

In order to obtain more reasonable failure modes and more precise surrounding rock pressures of deep-buried underground rectangular chambers, the failure mode of a “wedge-shaped collapse body + arc rotator + logarithmic spiral rotator” de...

Initial-boundary value problems for the generalized Benney-Lin equation posed on bounded intervals and on the right half-line were considered. The existence and uniqueness of global regular solutions on arbitrary intervals as well as their exponentia...

In this paper, we discuss the existence of normalized solutions for a class of the nonlinear elliptic systems with mixed-power nonlinearities on bounded domains. When the lower-order nonlinearity is $L^2$-subcritical and the leading term is $L^2$-critical,...

In the present article, we establish conditions for the asymptotic periodicity of bounded mild solutions in two distinct cases of evolution equations. The first class involves non-densely defined operators, while the second class incorporates densely...

This paper deals with the existence of bounded and locally Hölder continuous weak solutions of the following nonlinear fourth-order Dirichlet problem: ${\displaystyle \sum _{\left|\alpha \right|=1,2}}{(-1)}^{\left|\alpha \right|}{\mathrm{D}}^{\alpha }\left[A_{\alpha }(x,u,{\mathrm{D}}^{1}u,{\mathrm{D}}^{2}u)-E_{\alpha }\left(x\right) {\left|u\right|}^{\&}\right]$...

In this paper, we consider a time fractional diffusion system with a nonlinear memory term in a bounded domain. We mainly prove some blow-up and global existence results for this problem. Moreover, we also give the decay estimates of the global solut...

The main result of the paper establishes the existence of a bounded weak solution for a nonlinear Dirichlet problem exhibiting full dependence on the solution u and its gradient $\nabla u$ in the reaction term, which is driven by a p-Laplacian-type operator...

In this narrative review, the biological/biochemical impact (toxicity) of a large array of known individual uremic retention solutes and groups of solutes is summarized. We classified these compounds along their physico-chemical characteristics as sm...

This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing i...

The analytic solution for a general form of the Stefan problem with nonlinear temperature-dependent thermal parameters and a heat source the term is obtained. We prove the existence and uniqueness of the solution to the problem in the absence of a he...

We present a technique to solve the linear integer model with variable bounding. By using the continuous optimal solution of the linear integer model, the variable bounds for the basic variables are approximated and then used to calculate the optimal...

In this work, we obtain exact solutions and continuous numerical approximations for mixed problems of coupled systems of diffusion equations with delay. Using the method of separation of variables, and based on an explicit expression for the solution...

Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost...

We have analyzed solutions of bound states of a scalar particle in spacetime with torsion. In the first analysis, we investigate the confinement of a scalar particle in a cylindrical shell. In the second step, we investigate the Klein–Gordon os...

Indoxyl sulfate, closely related to indigo, a dye valued for it binding to cloth, has been recognized as a protein-bound solute bound to albumin, present in increased concentration in the serum of patients with impaired glomerular filtration (13). Th...

The present article concerns general mixed problems for nonlinear dispersive equations of any odd-orders posed on bounded intervals. The results on existence, uniqueness and exponential decay of solutions are presented.

In 2024, four papers that presented four different solution approaches for the knapsack problem with forfeits (KPF) appeared in the OR literature. However, none of these four solution approaches compared their performance to the other three on a stan...

In this paper, a dynamic multi-task scheduling prototype is proposed to improve the limited resource utilization in the vehicular networks (VNET) assisted by mobile edge computing (MEC). To ensure quality of service (QoS) and meet the growing data de...

In this article, we focus on examining the existence, uniqueness, and continuous dependence of solutions on initial data for a specific initial boundary value problem which mainly arises from one-dimensional quasi-static contact problems in nonlinear...

In this purely analytical analysis, we have investigated the effects of a point-like defect in a continuous medium on a diatomic molecule under the influence of small oscillations arising from the Lennard-Jones potential. In the search for bound-stat...

In this paper, the transport phenomena of synaptic electric impulses are considered. The FitzHugh–Nagumo and FitzHugh–Rinzel models appear mathematically appropriate for evaluating these scientific issues. Moreover, applications of such m...

(1) Background: This paper is devoted to the study of a class of semilinear initial boundary value problems of parabolic type. (2) Methods: We make use of fractional powers of analytic semigroups and the interpolation theory of compact linear operato...

Hemodiafiltration (HDF) combines diffusion and convection to enhance solute removal compared with hemodialysis (HD). While widely adopted in Europe and parts of Asia, uptake elsewhere remains limited due to regulatory, reimbursement, and infrastructu...

We investigate the effects of Lorentz symmetry violation (LSV) on a scalar particle via a non-minimal coupling in the Klein–Gordon equation within the charge–parity–time CPT-odd gauge sector. Through an analytical approach, we deriv...

Many hypotheses could explain the mortality decrease observed using hemodiafiltration, such as reduction of intradialytic hypotension and more efficient toxin removal. We led a systematic analysis of representative uremic toxin removal with hemodialy...

The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions $L\times H$. Start...

The delays and disruptions during the pandemic have awakened interest in the sustainability and resilience of production systems to emergencies. In that context, the deployment of smart technologies has emerged as an almost mandatory development orie...

In 1981, Foias, Guillopé and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier–Stokes equation. Such bounds are instructive in the numerical investigation of intermittency that is often observed in simul...

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity fie...

Under the uniform Hörmander hypothesis, we study the smoothness and exponential bounds of the density of the law of the solution of a stochastic differential equation (SDE) with locally Lipschitz drift that satisfies a monotonicity condition. We...

We first consider the damped wave inequality $\frac{{\partial }^{2}u}{\partial t^2}-\frac{{\partial }^{2}u}{\partial x^2}+\frac{\partial u}{\partial t}\ge x^{\sigma }{\left|u\right|}^p,t>0,x\in (0,L),$ where $L>0$, $\sigma \in \mathbb{R}$, and $p>1$, under the Dirichlet boundary conditions $\left(u\right(t,0),u(t,L\left)\right)=\left(f\right(t),g(t\left)\right),t\&g$...

The yield criterion of many metallic materials differs from the von Mises yield criterion. However, the available upper bound solutions are almost all restricted to this criterion. The objective of the present paper was to derive an upper bound solut...

Ion adsorption rare-earth (IARE) ores, a strategic metal resource, are extracted by leaching with ammonium sulfate [(NH4)₂SO₄] solution, our samples have ∑REO grades of 0.032–0.079% wt%. IARE sandstone, mudstone, clay, and strongly weathere...

This paper studies the uniqueness of the bounded solution to a new Cauchy problem of the fractional nonlinear partial integro-differential equation based on the multivariate Mittag–Leffler function as well as Banach’s contractive principl...

Various analytical solutions for computing production and injection-induced pressure changes in aquifers and oil reservoirs have been derived over the past century. All prior solutions assumed a constant well rate as the boundary condition. However,...

Many peptides and proteins are attached to or immersed in a biological membrane. In order to understand their function not only the structure but also their topology in the membrane is important. Solution NMR spectroscopy is one of the most often use...

We consider mixed Hamming packings, addressing the maximal cardinality of codes with a minimum codeword Hamming distance. We do not rely on any algebraic structure of the alphabets. We extend known-integer linear programming models of the problem to...